We look at the division of 354561 by 65 
Our goal is to divide 354561 by 65.

Moving on to step 1:
When dividing 3 by 65, we get 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Take the next digit (5) from the dividend and append it to 3, then repeat: 35 / 65

Going ahead to step 2:
The number 65 fits into 35 0 times, leaving a remainder of 35.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 35, we get 35.
Bring next digit (4) of the dividend behind the 35 and repeat the process: 354 / 65

Step 3:
354 divided by 65 is 5 with a remainder of 29.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
Deduct 325 from 354 and we're left with 29.
Append the next digit (5) from the dividend to 29 and continue with: 295 / 65

Moving on to step 4:
The number 65 fits into 295 4 times, leaving a remainder of 35.
The number 4 becomes the next digit in our result. 
Result so far: 54.0
The remainder is 35 after subtracting 260 from 295.
Include the next digit (6) from the dividend after 35, then repeat: 356 / 65

Going ahead to step 5:
356 divided by 65 is 5 with a remainder of 31.
The number 5 becomes the next digit in our result. 
Result so far: 545.0
The remainder is 31 after subtracting 325 from 356.
Fetch the next digit (1) from the dividend, attach it to 31 and continue: 311 / 65

Advancing to step 6:
311 divided by 65 is 4 with a remainder of 51.
The number 4 becomes the next digit in our result. 
Result so far: 5454.0
Subtract 260 from 311 to get 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Going ahead to step 7:
The number 65 fits into 510 7 times, leaving a remainder of 55.
Write down 7 as next digit of the result. 
Result so far: 5454.7
The remainder is 55 after subtracting 455 from 510.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Let's proceed to step 8:
65 can be fit into 550 8 times, resulting in a remainder of 30.
Put 8 as the next digit of the answer. 
Result so far: 5454.78
Subtracting 520 from 550 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 9:
If we divide 300 by 65, we get 4 and a remainder of 40.
The next digit of our result is 4. 
Result so far: 5454.784
Subtract 260 from 300 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 10:
If we divide 400 by 65, we get 6 and a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 5454.7846
Subtract 390 from 400 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 11:
100 divided by 65 is 1 with a remainder of 35.
Record the quotient 1 as the next digit in the result. 
Result so far: 5454.78461
Subtract 65 from 100 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 12:
65 goes into 350 5 times with a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 5454.784615
Subtracting 325 from 350 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 13:
If we divide 250 by 65, we get 3 and a remainder of 55.
Use 3 as the next digit of our solution. 
Result so far: 5454.7846153
Subtracting 195 from 250 leaves us with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Step 14:
The number 65 fits into 550 8 times, leaving a remainder of 30.
The number 8 becomes the next digit in our result. 
Result so far: 5454.78461538
Subtracting 520 from 550 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The quotient of the division is 5454.78461538, and the remainder is 3e-08.